Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 582)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.16403967840464902863.1	x^10 - x^9 + 254x^8 - 254x^7 + 23530x^6 - 23530x^5 + 960389x^4 - 960389x^3 + 16351644x^2 - 16351644x + 87151417	\( -\,3^{5}\cdot 11^{9}\cdot 31^{5} \)	$C_{10}$ (as 10T1)	$[2, 5288]$ (GRH)
10.0.28687182077984145408.1	x^10 - 2x^9 + 203x^8 - 322x^7 + 17152x^6 - 20444x^5 + 751955x^4 - 603934x^3 + 17082831x^2 - 6992754x + 160833331	\( -\,2^{15}\cdot 3^{5}\cdot 7^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	$[2, 6842]$ (GRH)
10.0.28688039019625283584.1	x^10 + 286x^8 + 29744x^6 + 1353352x^4 + 25133680x^2 + 130695136	\( -\,2^{15}\cdot 11^{9}\cdot 13^{5} \)	$C_{10}$ (as 10T1)	$[2, 6366]$ (GRH)
10.0.30094051633627471875.1	x^10 - x^9 + 287x^8 - 287x^7 + 30031x^6 - 30031x^5 + 1383383x^4 - 1383383x^3 + 26517063x^2 - 26517063x + 157212199	\( -\,3^{5}\cdot 5^{5}\cdot 7^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[2, 2, 2882]$ (GRH)
10.0.43994352468921100983.1	x^10 - 3x^9 + 224x^8 - 532x^7 + 20710x^6 - 36564x^5 + 985774x^4 - 1151813x^3 + 24145816x^2 - 14014089x + 243663793	\( -\,3^{5}\cdot 11^{8}\cdot 61^{5} \)	$C_{10}$ (as 10T1)	$[13640]$ (GRH)
10.0.45209592896296812544.1	x^10 - 2x^9 + 223x^8 - 354x^7 + 20624x^6 - 24596x^5 + 986595x^4 - 792094x^3 + 24385063x^2 - 9962410x + 249060239	\( -\,2^{15}\cdot 11^{8}\cdot 23^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2, 820]$ (GRH)
10.0.54488934738121076831.1	x^10 - 3x^9 + 234x^8 - 556x^7 + 22570x^6 - 39880x^5 + 1119450x^4 - 1309413x^3 + 28539794x^2 - 16586309x + 299407151	\( -\,11^{8}\cdot 191^{5} \)	$C_{10}$ (as 10T1)	$[17953]$ (GRH)
10.0.58673283984691200000.1	x^10 + 330x^8 + 39600x^6 + 2079000x^4 + 44550000x^2 + 267300000	\( -\,2^{15}\cdot 3^{5}\cdot 5^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[2, 2, 2962]$ (GRH)
10.0.60438619802379121875.1	x^10 - 3x^9 + 239x^8 - 568x^7 + 23530x^6 - 41592x^5 + 1190596x^4 - 1393337x^3 + 30949039x^2 - 17997705x + 330865051	\( -\,3^{5}\cdot 5^{5}\cdot 11^{8}\cdot 13^{5} \)	$C_{10}$ (as 10T1)	$[2, 8210]$ (GRH)
10.0.66897034053072122119.1	x^10 - 3x^9 + 244x^8 - 580x^7 + 24510x^6 - 43340x^5 + 1264694x^4 - 1480773x^3 + 33507652x^2 - 19497305x + 364912549	\( -\,11^{8}\cdot 199^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 22, 198]$ (GRH)
10.0.69126185467638109184.1	x^10 + 341x^8 + 42284x^6 + 2293907x^4 + 50793655x^2 + 314920661	\( -\,2^{10}\cdot 11^{9}\cdot 31^{5} \)	$C_{10}$ (as 10T1)	$[2, 7294]$ (GRH)
10.0.73896125949393369083.1	x^10 - 3x^9 + 249x^8 - 592x^7 + 25510x^6 - 45124x^5 + 1341804x^4 - 1571793x^3 + 36221681x^2 - 21088709x + 401706293	\( -\,7^{5}\cdot 11^{8}\cdot 29^{5} \)	$C_{10}$ (as 10T1)	$[16564]$ (GRH)
10.0.84233087151233292459.1	x^10 - x^9 + 353x^8 - 353x^7 + 45409x^6 - 45409x^5 + 2568545x^4 - 2568545x^3 + 60240225x^2 - 60240225x + 429338977	\( -\,3^{5}\cdot 11^{9}\cdot 43^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2, 2, 366]$ (GRH)
10.0.89650715035413264931.1	x^10 - 3x^9 + 259x^8 - 616x^7 + 27570x^6 - 48800x^5 + 1505300x^4 - 1764873x^3 + 42140779x^2 - 24561689x + 484190191	\( -\,11^{8}\cdot 211^{5} \)	$C_{10}$ (as 10T1)	$[13665]$ (GRH)
10.0.91795371948772692992.1	x^10 - 2x^9 + 258x^8 - 410x^7 + 27470x^6 - 32786x^5 + 1506247x^4 - 1208692x^3 + 42497682x^2 - 17315000x + 493477489	\( -\,2^{10}\cdot 11^{8}\cdot 53^{5} \)	$C_{10}$ (as 10T1)	$[16566]$ (GRH)
10.0.98127869835026633063.1	x^10 - x^9 + 364x^8 - 364x^7 + 48280x^6 - 48280x^5 + 2815429x^4 - 2815429x^3 + 68041084x^2 - 68041084x + 498530407	\( -\,7^{5}\cdot 11^{9}\cdot 19^{5} \)	$C_{10}$ (as 10T1)	$[2, 8656]$ (GRH)
10.0.98476766684475884375.2	x^10 - 3x^9 + 264x^8 - 628x^7 + 28630x^6 - 50692x^5 + 1591806x^4 - 1867077x^3 + 45358544x^2 - 26450825x + 530225081	\( -\,5^{5}\cdot 11^{8}\cdot 43^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2, 770]$ (GRH)
10.0.107984657578733286219.1	x^10 - 3x^9 + 269x^8 - 640x^7 + 29710x^6 - 52620x^5 + 1681564x^4 - 1973153x^3 + 48757117x^2 - 28446885x + 579695929	\( -\,3^{5}\cdot 11^{8}\cdot 73^{5} \)	$C_{10}$ (as 10T1)	$[13420]$ (GRH)
10.0.109705577585055727616.1	x^10 + 374x^8 + 50864x^6 + 3026408x^4 + 73498480x^2 + 499789664	\( -\,2^{15}\cdot 11^{9}\cdot 17^{5} \)	$C_{10}$ (as 10T1)	$[2, 7294]$ (GRH)
10.0.113798621747061378787.1	x^10 - x^9 + 375x^8 - 375x^7 + 51239x^6 - 51239x^5 + 3077647x^4 - 3077647x^3 + 76576127x^2 - 76576127x + 576365791	\( -\,11^{9}\cdot 137^{5} \)	$C_{10}$ (as 10T1)	$[13324]$ (GRH)
10.0.118213151760871933183.1	x^10 - 3x^9 + 274x^8 - 652x^7 + 30810x^6 - 54584x^5 + 1774634x^4 - 2083173x^3 + 52343146x^2 - 30553829x + 632791543	\( -\,11^{8}\cdot 223^{5} \)	$C_{10}$ (as 10T1)	$[17507]$ (GRH)
10.0.126816085896438400000.1	x^10 + 385x^8 + 53900x^6 + 3301375x^4 + 82534375x^2 + 577740625	\( -\,2^{10}\cdot 5^{5}\cdot 7^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[2, 2, 5522]$ (GRH)
10.0.129202455411534814067.2	x^10 - 3x^9 + 279x^8 - 664x^7 + 31930x^6 - 56584x^5 + 1871076x^4 - 2197209x^3 + 56123399x^2 - 32775689x + 689707523	\( -\,11^{8}\cdot 227^{5} \)	$C_{10}$ (as 10T1)	$[27275]$ (GRH)
10.0.131410397716621007391.1	x^10 - x^9 + 386x^8 - 386x^7 + 54286x^6 - 54286x^5 + 3355661x^4 - 3355661x^3 + 85890036x^2 - 85890036x + 663630661	\( -\,3^{5}\cdot 11^{9}\cdot 47^{5} \)	$C_{10}$ (as 10T1)	$[2, 13136]$ (GRH)
10.0.132073508910190814208.1	x^10 - 2x^9 + 278x^8 - 442x^7 + 31822x^6 - 37994x^5 + 1872095x^4 - 1501924x^3 + 56562186x^2 - 23016264x + 701996041	\( -\,2^{10}\cdot 3^{5}\cdot 11^{8}\cdot 19^{5} \)	$C_{10}$ (as 10T1)	$[2, 12710]$ (GRH)
10.0.144072603981062766592.1	x^10 - 2x^9 + 283x^8 - 450x^7 + 32960x^6 - 39356x^5 + 1971987x^4 - 1581982x^3 + 60565807x^2 - 24638290x + 763786979	\( -\,2^{15}\cdot 11^{8}\cdot 29^{5} \)	$C_{10}$ (as 10T1)	$[11842]$ (GRH)
10.0.151138176325959246875.1	x^10 - x^9 + 397x^8 - 397x^7 + 57421x^6 - 57421x^5 + 3649933x^4 - 3649933x^3 + 96028813x^2 - 96028813x + 761156749	\( -\,5^{5}\cdot 11^{9}\cdot 29^{5} \)	$C_{10}$ (as 10T1)	$[2, 6248]$ (GRH)
10.0.153631684573303646875.1	x^10 - 3x^9 + 289x^8 - 688x^7 + 34230x^6 - 60692x^5 + 2074316x^4 - 2437617x^3 + 64294249x^2 - 37580645x + 815817661	\( -\,5^{5}\cdot 11^{8}\cdot 47^{5} \)	$C_{10}$ (as 10T1)	$[27962]$ (GRH)
10.0.167159470199251882319.1	x^10 - 3x^9 + 294x^8 - 700x^7 + 35410x^6 - 62800x^5 + 2181234x^4 - 2564133x^3 + 68698982x^2 - 40172165x + 885438059	\( -\,11^{8}\cdot 239^{5} \)	$C_{10}$ (as 10T1)	$[18825]$ (GRH)
10.0.173167149654912345559.1	x^10 - x^9 + 408x^8 - 408x^7 + 60644x^6 - 60644x^5 + 3960925x^4 - 3960925x^3 + 107039780x^2 - 107039780x + 869823307	\( -\,11^{9}\cdot 149^{5} \)	$C_{10}$ (as 10T1)	$[22682]$ (GRH)
10.0.185391839210597561344.1	x^10 - 2x^9 + 298x^8 - 474x^7 + 36494x^6 - 43586x^5 + 2292855x^4 - 1839124x^3 + 73858498x^2 - 30021400x + 975695489	\( -\,2^{10}\cdot 11^{8}\cdot 61^{5} \)	$C_{10}$ (as 10T1)	$[5, 7230]$ (GRH)
10.0.191316358585955418112.1	x^10 + 418x^8 + 63536x^6 + 4225144x^4 + 114682480x^2 + 871586848	\( -\,2^{15}\cdot 11^{9}\cdot 19^{5} \)	$C_{10}$ (as 10T1)	$[82, 164]$ (GRH)
10.0.197072600565005618167.1	x^10 - 3x^9 + 304x^8 - 724x^7 + 37830x^6 - 67124x^5 + 2405966x^4 - 2830149x^3 + 78183304x^2 - 45754889x + 1038929473	\( -\,11^{8}\cdot 13^{5}\cdot 19^{5} \)	$C_{10}$ (as 10T1)	$[39246]$ (GRH)
10.0.201094357724038135808.1	x^10 - 2x^9 + 303x^8 - 482x^7 + 37712x^6 - 45044x^5 + 2407075x^4 - 1930654x^3 + 78740871x^2 - 31997834x + 1055928511	\( -\,2^{15}\cdot 11^{8}\cdot 31^{5} \)	$C_{10}$ (as 10T1)	$[18040]$ (GRH)
10.0.210528769967490760704.1	x^10 + 186x^8 + 8928x^6 + 154008x^4 + 843696x^2 + 241056	\( -\,2^{15}\cdot 3^{5}\cdot 31^{9} \)	$C_{10}$ (as 10T1)	$[2, 6666]$ (GRH)
10.0.213555169438713585131.1	x^10 - 3x^9 + 309x^8 - 736x^7 + 39070x^6 - 69340x^5 + 2523900x^4 - 2969793x^3 + 83277749x^2 - 48754949x + 1123270721	\( -\,11^{8}\cdot 251^{5} \)	$C_{10}$ (as 10T1)	$[28987]$ (GRH)
10.0.217849796305279497216.1	x^10 + 429x^8 + 66924x^6 + 4567563x^4 + 127239255x^2 + 992466189	\( -\,2^{10}\cdot 3^{5}\cdot 11^{9}\cdot 13^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 9124]$ (GRH)
10.0.224922254746594335887.1	x^10 - x^9 + 430x^8 - 430x^7 + 67354x^6 - 67354x^5 + 4634917x^4 - 4634917x^3 + 131874172x^2 - 131874172x + 1124340361	\( -\,11^{9}\cdot 157^{5} \)	$C_{10}$ (as 10T1)	$[28116]$ (GRH)
10.0.231122583503450409375.1	x^10 - 3x^9 + 314x^8 - 748x^7 + 40330x^6 - 71592x^5 + 2645626x^4 - 3113957x^3 + 88617154x^2 - 51900165x + 1213001791	\( -\,3^{5}\cdot 5^{5}\cdot 11^{8}\cdot 17^{5} \)	$C_{10}$ (as 10T1)	$[2, 8430]$ (GRH)
10.0.249827534298605990419.1	x^10 - 3x^9 + 319x^8 - 760x^7 + 41610x^6 - 73880x^5 + 2771204x^4 - 3262713x^3 + 94209247x^2 - 55195145x + 1308376939	\( -\,7^{5}\cdot 11^{8}\cdot 37^{5} \)	$C_{10}$ (as 10T1)	$[25420]$ (GRH)
10.0.254687846410025600000.1	x^10 - 2x^9 + 318x^8 - 506x^7 + 41486x^6 - 49562x^5 + 2772367x^4 - 2223364x^3 + 94847418x^2 - 38515496x + 1328784601	\( -\,2^{10}\cdot 5^{5}\cdot 11^{8}\cdot 13^{5} \)	$C_{10}$ (as 10T1)	$[2, 15620]$ (GRH)
10.0.255072445858418756491.1	x^10 - x^9 + 441x^8 - 441x^7 + 70841x^6 - 70841x^5 + 4998841x^4 - 4998841x^3 + 145798841x^2 - 145798841x + 1272198841	\( -\,7^{5}\cdot 11^{9}\cdot 23^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2, 2, 1084]$ (GRH)
10.0.269724392565300429383.1	x^10 - 3x^9 + 324x^8 - 772x^7 + 42910x^6 - 76204x^5 + 2900694x^4 - 3416133x^3 + 100061876x^2 - 58644569x + 1409658293	\( -\,11^{8}\cdot 263^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 5330]$ (GRH)
10.0.290869234586803326267.1	x^10 - 3x^9 + 329x^8 - 784x^7 + 44230x^6 - 78564x^5 + 3034156x^4 - 3574289x^3 + 106183009x^2 - 62253189x + 1517115973	\( -\,3^{5}\cdot 11^{8}\cdot 89^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2, 1982]$ (GRH)
10.0.313319868528953077231.1	x^10 - 3x^9 + 334x^8 - 796x^7 + 45570x^6 - 80960x^5 + 3171650x^4 - 3737253x^3 + 112580734x^2 - 66025829x + 1631028211	\( -\,11^{8}\cdot 271^{5} \)	$C_{10}$ (as 10T1)	$[11, 2255]$ (GRH)
10.0.315559002857825599488.1	x^10 + 462x^8 + 77616x^6 + 5704776x^4 + 171143280x^2 + 1437603552	\( -\,2^{15}\cdot 3^{5}\cdot 7^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[2, 2, 7342]$ (GRH)
10.0.343310346056253920256.1	x^10 - 2x^9 + 338x^8 - 538x^7 + 46798x^6 - 55922x^5 + 3314471x^4 - 2657716x^3 + 120020466x^2 - 48695928x + 1777401361	\( -\,2^{10}\cdot 3^{5}\cdot 11^{8}\cdot 23^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2, 2, 1004]$ (GRH)
10.0.354957535978859635712.1	x^10 + 473x^8 + 81356x^6 + 6122039x^4 + 188034055x^2 + 1617092873	\( -\,2^{10}\cdot 11^{9}\cdot 43^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2, 2, 726]$ (GRH)
10.0.365396751549062507263.1	x^10 - x^9 + 474x^8 - 474x^7 + 81830x^6 - 81830x^5 + 6203869x^4 - 6203869x^3 + 194237924x^2 - 194237924x + 1811330797	\( -\,11^{9}\cdot 173^{5} \)	$C_{10}$ (as 10T1)	$[11, 3982]$ (GRH)
10.0.368919522607820800000.1	x^10 - 2x^9 + 343x^8 - 546x^7 + 48176x^6 - 57572x^5 + 3460227x^4 - 2774494x^3 + 127028023x^2 - 51528826x + 1906566551	\( -\,2^{15}\cdot 5^{5}\cdot 7^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	$[2, 12382]$ (GRH)